Laws of
Motion
Newton's Laws of Motion
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Newton's second
law is all about momentum. We have seen that momentum
is the product of mass (m) and velocity (v). So what
does momentum depend upon? In fact it does not depend
upon mass. It depends upon the force applied on the
body.
Second
Law of Motion: The rate of change of
momentum of a moving body is proportional to and in
the same direction as the force acting on it ie F =
d(mv)/dt, where F is the applied force, v is the
velocity of the body, and m its mass. if mass remains
constant, F = mdv/dt or F =ma, where a is the
acceleration The direction of acceleration is the
same as that of F.
As F = ma it
follows that for a fixed mass, greater the force,
greater the acceleration. The harder you throw a ball
the greater will be its acceleration and the further
it will go!
How do we
explain the behavior of a ball which is hit by a bat
instead of being thrown. In the case of a bat the
force acts for an extremely short duration. The
effect of this force is called an impulse. Which
gives rise to the question.
What is
impulse?
Impulse
(J): It is the product of a force F and
the time t for which it acts. If the force is variable, the impulse
is the integral of Fdt from to
to t1. The impulse of a
force acting for a given interval is equal to the
change in momentum produced over the interval. J =m(v1
- v0), assuming that mass
(m) remains constant while the velocity changes from
v0 to v1.
Numerical
problems:
A bullet of
mass 0.04 kg moving with a speed of 90 m/s enters a
heavy wooden block and is stopped after it penetrates
60 cm into the block. What is the average resistive
force exerted by the block on the bullet?
u = 90 m/s, v =
0, S = 60 cm = 0.6m
v2 -
u2 = 2as
-902
= 2 x a x 0.6
a = -902
/ 2 x 0.6 = -6750 m/s2
retarding force
= m a = 0.04 x 6750 = 270 N
A base ball of
mass 200 g moving with a velocity of 15 m/s is
brought to rest by a player in 0.05 second. What is
the impulse of the ball and the average force applied
by the player?
m = 0.2 kg, u =
15 m/s, v = 0
Change in
momentum = m(v - u) = -0.2 x 15 = -3 Ns
As change in
momentum = impulse = -3 Ns
Impulse(J) =
average force(F) x time(t)
F = J/t =
3/0.05 = 60 N
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